FBX not showing current version of mesh
I had accidentally changed the mesh in a custom shape key rather than on the basis shape key - meaning the head enlarged when she blinked! I needed her head to be enlarged for every animation. For future reference, if you want to edit the mesh for all animations (shape keys), ensure you have basis shape key selected in object mode, then go into edit mode. As I had already made the mistake of editing another shape key, I just deleted it, edited the basis key as I should have done, and recreated the blinking shape key.